Conventionally, de-inking of fiber suspensions of used paper is performed in so-called flotation cells, in which air is supplied naturally or is forced into the suspension in such a way that an intimate mixture of air and suspension occurs and dispersion of the air through the suspension results. The subsequent separation of air, together with the collectors and carriers, to which the printing ink particles adhere, from the suspension occurs as a result of the buoyancy of the collectors and carriers which form a foam. The foam in which the printing ink particles are carried floats and is then skimmed from the open vessel off the surface of the suspension. The drawback of this process is that under optimal conditions, the flotation cells can operate only at material densities of about 1%. Higher material densities decrease the effectiveness of the process performed in these cells. Furthermore, the power consumption of the conventional process is relatively high.